It's the bay area, but we break it up into South bay, and East bay to easily pinpoint the location we are referring to. "She's from somewhere in the East bay",

It's the bay area, but we break it up into South bay, and East bay to easily pinpoint the location we are referring to. "She's from somewhere in the East bay", but it's still the bay area; But you don't use it in the following way, "I'm going to the South bay". You would just say, "I'm going to Cupertino/Ssn Jose/etc..." If you're referring to San Francisco, you would just say the city or San Francisco. If you say "frisko", everyone would know you're not from San Francisco.